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May 2010
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Theoretical physicists use mathematics to describe certain aspects of Nature. Sir Isaac Newton was the first theoretical physicist, although in his own time his profession was called “natural philosophy”.
. By Newton’s era people had already used algebra and geometry to build marvelous works of architecture, including the great cathedrals of Europe, but algebra and geometry only describe things that are sitting still. In order to describe things that are moving or changing in some way, Newton invented calculus.
. The most puzzling and intriguing moving things visible to humans have always been been the sun, the moon, the planets and the stars we can see in the night sky. Newton’s new calculus, combined with his “Laws of Motion”, made a mathematical model for the force of gravity that not only described the observed motions of planets and stars in the night sky, but also of swinging weights and flying cannonballs in England.
. Today’s theoretical physicists are often working on the boundaries of known mathematics, sometimes inventing new mathematics as they need it, like Newton did with calculus.
. Newton was both a theorist and an experimentalist. He spent many many long hours, to the point of neglecting his health, observing the way Nature behaved so that he might describe it better. The so-called “Newton’s Laws of Motion” are not abstract laws that Nature is somehow forced to obey, but the observed behavior of Nature that is described in the language of mathematics. In Newton’s time, theory and experiment went together.
. Today the functions of theory and observation are divided into two distinct communities in physics. Both experiments and theories are much more complex than back in Newton’s time. Theorists are exploring areas of Nature in mathematics that technology so far does not allow us to observe in experiments. Many of the theoretical physicists who are alive today may not live to see how the real Nature compares with her mathematical description in their work. Today’s theorists have to learn to live with ambiguity and uncertainty in their mission to describe Nature using math.


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